Quadratic Formula Calculator

Roots of ax² + bx + c = 0 — real or complex — with the discriminant.

Quick answer: Solve quadratic equations instantly online. Free quadratic formula calculator finds real and complex roots with step-by-step discriminant math.

x₁2
x₂1
Discriminant1 (two real roots)

computed locally — nothing leaves your browser

Solve any quadratic equation: enter the coefficients and get both roots, including complex roots when the parabola never crosses the x-axis.

How it works

  1. Identify the coefficients a, b, and c in your ax² + bx + c = 0 equation.
  2. Enter the coefficients into the calculator.
  3. Read the calculated roots and discriminant value.

Frequently asked questions

What does the discriminant mean visually?

It counts x-intercepts: 2 crossings, 1 touch, or none (the parabola floats above or below the axis).

What if a = 0?

Then it's linear, not quadratic — the tool solves bx + c = 0 instead and tells you.

What are complex roots good for?

They appear throughout physics and engineering — oscillations, AC circuits, control systems.

What do complex roots mean?

If the discriminant (b²−4ac) is negative, the parabola does not cross the x-axis and the roots are complex numbers — the tool will show them in a+bi form.

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